2.1.1 RasterLayer

# Chunk 1
# #1
e <- extent(c("xmin" = 27, "xmax" = 29, "ymin" = -16, "ymax" = -14))  
#
# #2
r <- raster(x = e, res = 0.25, crs = crs(districts))
#
# #3            
set.seed(1)  
values(r) <- sample(1:100, size = ncell(r), replace = TRUE)  # 3
# r[] <- sample(1:100, size = ncell(r), replace = TRUE) 
# r <- setValues(x = r, values = sample(1:100, size = ncell(r), replace = TRUE))

par(mar = c(0, 0, 0, 4))
plot(st_geometry(districts), col = "grey", reset = FALSE)
plot(r, add = TRUE)

We just used several functions from the raster package to create a random raster named r that has a 1/4 degree resolution and covers an area of 2 X 2 degrees in southern Zambia. This particular raster is a temporary one that lives in memory.

Let’s walk through the labelled code. In # 1, we use raster’s extent function to define the boundaries of the raster, and then in # 2 use the raster function to create a raster from the resulting Extent object e, assigning a CRS using the “crs” argument, which in turn uses raster’s crs to extract the crs from districts (#3). crs is similar to sf::st_crs, but outputs a different class of object that can’t be used by raster. The raster function can create a raster from many different types of input objects (passed to argument “x”), per ?raster:

filename (character), Extent, Raster, SpatialPixels, SpatialGrid*, object, ‘image’, matrix, im, or missing. Supported file types are the ‘native’ raster package format and those that can be read via rgdal

Line # 2 creates an empty raster r with no cell values, so in # 3 we assign some randomly selected values into r. Note the method of assignment, using the values function; there are two other lines commented out below # 3 that show different ways of doing the same job.

The plot of r over districts uses the plot method defined for raster* objects. Note that it automatically creates a continuous legend, and also note that raster::plot can work with sf::plot.

Let’s look now at the structure of the object r.

# Chunk 2
r
#> class      : RasterLayer 
#> dimensions : 8, 8, 64  (nrow, ncol, ncell)
#> resolution : 0.25, 0.25  (x, y)
#> extent     : 27, 29, -16, -14  (xmin, xmax, ymin, ymax)
#> crs        : +proj=longlat +datum=WGS84 +no_defs
#> source     : memory
#> names      : layer 
#> values     : 1, 100  (min, max)
class(r)
#> [1] "RasterLayer"
#> attr(,"package")
#> [1] "raster"
typeof(r)
#> [1] "S4"
slotNames(r)
#>  [1] "file"     "data"     "legend"   "title"    "extent"   "rotated"  "rotation" "ncols"   
#>  [9] "nrows"    "crs"      "history"  "z"
values(r)
#>  [1]  68  39   1  34  87  43  14  82  59  51  97  85  21  54  74   7  73  79  85  37  89  37  34  89
#> [25]  44  79  33  84  35  70  74  42  38  20  28  20  44  87  70  40  44  25  70  39  51  42   6  24
#> [49]  32  14   2  45  18  22  78  65  70  87  70  75  81 100  13  40
# slot(slot(r, "data"), "values")  # identical to values(r)
res(r)
#> [1] 0.25 0.25

r is an S4 object that has fairly different slots compared to sf objects. We are not going to go into all of them, but it is useful to know the @file, @data, @extent, and @crs slots. @file itself holds a number of slots, but you should know the @file@name slot, which contains the file name and path for grids that that are read in from disk (it is empty in the case of r, since it is held in memory). @data contains many slots also, but the main one of interest is the @data@values slot, which can be accessed with the values function directly, or less directly using slot (both approaches are shown above). Interestingly, the resolution information is not stored in any of the slots of r, but rather calculated from the @extent and @ncols and @nrows slots by the res function.

2.1.2 RasterStack and RasterBrick

We have just seen how to create a RasterLayer and learned a bit about the structure of this kind of object, which is two-dimensional. We are now going to learn about three-dimensional rasters, which come in two flavors: RasterStack and RasterBrick. Before we proceed, we first need to create some new data.

# Chunk 3
r2 <- r > 50
r3 <- r
set.seed(1)
values(r3) <- rnorm(n = ncell(r3), mean = 10, sd = 2)
l <- list(r, r2, r3)

We used r to create two new rasters, r2 and r3. r2 was made by using a logical operator (>) to find the locations where r’s values exceed 50, creating a binary raster where 1 indicates the matching pixels, and 0 those that don’t. r3 was made by using r as a template, then overwriting the values with numbers generated randomly from a normal distribution (rnorm). These were then combined into list l.

# Chunk 4
s <- stack(l)
# s <- stack(r, r2, r3)  # also works
names(s) <- c("r", "r2", "r3")
s
#> class      : RasterStack 
#> dimensions : 8, 8, 64, 3  (nrow, ncol, ncell, nlayers)
#> resolution : 0.25, 0.25  (x, y)
#> extent     : 27, 29, -16, -14  (xmin, xmax, ymin, ymax)
#> crs        : +proj=longlat +datum=WGS84 +no_defs 
#> names      :         r,        r2,        r3 
#> min values :    1.0000,    0.0000,    5.5706 
#> max values : 100.00000,   1.00000,  14.80324

b <- brick(s)
b
#> class      : RasterBrick 
#> dimensions : 8, 8, 64, 3  (nrow, ncol, ncell, nlayers)
#> resolution : 0.25, 0.25  (x, y)
#> extent     : 27, 29, -16, -14  (xmin, xmax, ymin, ymax)
#> crs        : +proj=longlat +datum=WGS84 +no_defs 
#> source     : memory
#> names      :         r,        r2,        r3 
#> min values :    1.0000,    0.0000,    5.5706 
#> max values : 100.00000,   1.00000,  14.80324

plot(b, nr = 1)

In the preceding code blocks, we use l to create a RasterStack and RasterBrick. These are very similar things, but have a few key differences. A RasterStack is a series of rasters that have the same extent and resolution, which are “stacked” on top of one another in the order that they are given in the input list. The stacked layers can from any number of files stored in different areas on disk. A RasterBrick does the same thing (stacks RasterLayers on top of one another), but is more restrictive because the layers, if read off disk, must be contained within a single file. This makes the RasterBrick less flexible than the RasterStack, but it has the advantage of faster processing times (according to ?brick).

Applying plot to a stack or brick results in the automatic plotting of each layer into its own sub-window, with coordinates along the plot axes. You can specify numbers of rows and columns in your plotting device using the “nc” and “nr” arguments to raster::plot.

Here’s a more informative (by putting it over a map of Zambia) way of plotting the layers in s (works for b also):

# Chunk 5
par(mfrow = c(1, 3), mar = c(0, 0, 0, 4))
for(i in 1:nlayers(s)) {
  districts %>% st_geometry %>% plot(col = "grey")
  plot(s[[i]], add = TRUE)
}

2.3.1 Vector to raster

We have several vector datasets that come with geospaar which we can rasterize, starting with the district boundaries.

# Chunk 7
# #1
zamr <- raster(x = extent(districts), crs = crs(districts), res = 0.1)
values(zamr) <- 1:ncell(zamr)
#
# #2
districts <- districts %>% mutate(ID = 1:nrow(.))
distsr <- districts %>% rasterize(x = ., y = zamr, field = "ID") %>% print()
#> class      : RasterLayer
#> dimensions : 98, 117, 11466  (nrow, ncol, ncell)
#> resolution : 0.1, 0.1  (x, y)
#> extent     : 21.99978, 33.69978, -18.02621, -8.226213  (xmin, xmax, ymin, ymax)
#> crs        : +proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0
#> source     : memory
#> names      : layer
#> values     : 1, 72  (min, max)

par(mar = c(0, 0, 0, 4))
plot(distsr, axes = FALSE, box = FALSE)

In #1, we took an initial step to define a raster (zamr) that has the properties of resolution (0.1 decimal degrees), CRS, and extent that we want our rasterized vector to have. We set the extent of this raster to that of districts, using extent to get the bounding box coordinates (extent retrieves the same parameters as sf::st_bbox, but the output is in a different format).

In #2, we use rasterize to (as the name says) rasterize districts. The “y” argument is where we feed in zamr, the raster object that is the “target” for rasterizing districts. The “field” argument supplies the column names of the values that we want rasterized. In this case, we have to first create an “ID” variable for districts, in order to give an integer for each district name, as the district names (a character variable) cannot be written to the raster. Notice that we have constructed this as a pipeline (with print as the last step, to show the raster metadata). The commented out code below it shows how it can be done with more conventional syntax.

Our plot removes the coordinate-labelled axes and box that otherwise drawn around raster plots by default.

Next we rasterize the farmers dataset, which requires a little more prep to be meaningful:

# Chunk 8
# #1
zamr2 <- raster(x = extent(districts), crs = crs(districts), res = 0.25)
values(zamr2) <- 1:ncell(zamr2)

# #2
farmersr <- farmers %>% distinct(uuid, .keep_all = TRUE) %>% 
  dplyr::select(x, y) %>% mutate(count = 1) %>% 
  st_as_sf(coords = c("x", "y"), crs = 4326) %>% 
  rasterize(x = ., y = zamr2, field = "count", fun = sum) %>% print()
#> class      : RasterLayer 
#> dimensions : 39, 47, 1833  (nrow, ncol, ncell)
#> resolution : 0.25, 0.25  (x, y)
#> extent     : 21.99978, 33.74978, -17.97621, -8.226213  (xmin, xmax, ymin, ymax)
#> crs        : +proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0 
#> source     : memory
#> names      : layer 
#> values     : 1, 152  (min, max)

# #3
par(mar = c(0, 0, 1, 4))
districts %>% st_union %>% 
  plot(col = "grey", border = "grey", 
       main = expression(paste("N farmers per 0.25", degree, " cell")))
plot(farmersr, add = TRUE)

In #1, we create a coarser scale (0.25 degree) version of zamr (zamr2), because we want our final raster to count how many farmers responding to our survey are found in each grid cell. The resolution of 0.1 degrees used for zamr is a bit too fine to convey the information nicely in a plot.

In #2, we do the rasterization as part of a pipeline. The first two lines prepare the farmers dataset. Recall that farmers consists of weekly reporting data sent to us by a large number of farmers, which means that we have multiple reports sent by the same farmer (and thus repeated coordinates for each farmer). So we need to reduce farmers down to just one row for each individual farmer, so that we have just a single set of coordinates for each. We do that by using distinct on the uuid variable, using .keep_all = TRUE so that we retain the coordinates, and add a new count variable (which assigns a value of 1 to each farmer) before converting farmers to sf in the third line. We then rasterize the count variable, using the sum function to aggregate the number of farmers per 0.25\(\circ\) grid cell.

The resulting plot (#3) shows that most cells have less than 20 farmers. We add an extra plot decoration step, using expression with paste to add a superscript degree symbol to our plot title.

You can also rasterize line features, much as we did for points and polygons, but rasterize is exceedingly slow for lines, so we are not doing that here. However, there is code below that shows how one could so that with the roads dataset (subset to roads greater than 100 km long):

# Chunk 9
roadsr <- roads %>% filter(as.numeric(st_length(.)) > 1000000) %>% 
  mutate(ID = 1:nrow(.)) %>% st_transform(crs = 4326) %>% 
  rasterize(., zamr, field = "ID")

2.3.2 Raster to vector

raster gives us functions that allow us to transform rasters to vectors.

# Chunk 10
# #1
dists_fromr <- rasterToPolygons(x = distsr, dissolve = TRUE) %>% st_as_sf

# #2
farmers_fromr <- rasterToPoints(x = farmersr, spatial = TRUE) %>% st_as_sf

par(mar = c(0, 0, 0, 0))
dists_fromr %>% st_geometry %>% plot(col = topo.colors(n = nrow(districts)))
farmers_fromr %>% plot(pch = 20, col = "red", add = TRUE)

Vectorizing rasters and vectorizing back again means that you end up with lower resolution vectors if the raster is fairly coarse. You will note that this has occurred here, both in converting the rasterized districts back to polygons (#1) and the rasterized farmer counts back to points (#2). There are several things to note here. First, we used different functions for vectorizing polygons and points. Second, we piped each vectorization output to st_as_sf, because the endresult of the rasterTo* functions is an sp object, so the extra coerces those to sf.

2.5.1 Questions

1. What is a primary difference between sf and s4 object classes?

2. What function should you use to read and write a multi-layer raster?

3. What are the difference between stack and brick?

4. What class of object do raster’s vectorization functions produce?

2.5.2 Code

1. Create a new raster r4, using r3 (above) as a template. Update the values of r4 using numbers randomly selected from a uniform distribution ranging between 0 and 1. Create another raster r5 by finding the values greater than 0.5 in r4. Recreate the list l with r, r2, r3, r4, and r5, and then create and plot stack s2.

2. Create a new brick b2 by applying the brick function to s2 and writing it out to disk as b2.tif, specifying the path to your notebooks/data folder.

3. Following the steps in Chunk 8, recreate farmersr by re-rasterizing farmers at a 0.2 degree resolution. Plot the result.

4. Project the new 0.2 degree resolution farmersr to an Albers projection with a target resolution of 20 km (20,000 m), calling it farmersr_alb. Chunk 11 is your guide, but reproject using a bilinear rather than nearest neighbor interpolation (see ?projectRaster). Make a two panel plot comparing farmersr on the left, plotted over the unioned districts of Zambia in grey, with farmersr_alb on the right, plotted over the unioned districts of Zambia in grey (and transformed to Albers). Code in Chunks 8 and 11 can help.

5. Convert distsr to an sf polygons object, using rasterToPolygons with dissolve = TRUE. Plot the result without coercing to st_geometry.

3.1.1 Masking

We are interested in the rainfall data within Zambia’s borders, so we need to mask out the values of chirps that fall outside of Zambia:

# Chunk 16
test_m <- mask(x = chirps[[1]], mask = districts)
par(mar = c(0, 0, 0, 4))
plot(test_m, axes = FALSE, box = FALSE)  

In the code above, we use the districts data to mask out the portions of chirps (the first day in the time series only) falling outside of Zambia. Let’s apply that to the entire chirps dataset:

# Chunk 17
chirpsz <- mask(x = chirps, mask = districts)

set.seed(1)
ind <- sample(1:nlayers(chirpsz), size = 3)
plot(chirpsz[[ind]], axes = FALSE, box = FALSE, nr = 1)

The new chirpsz dataset contains all rainfall days with the values outside of Zambia converted to NA. The three plots are randomly selected from the layers of chirpsz, as a check to confirm that the masking was applied to all layers.

3.1.2 Cropping

If we need to chop a raster down to a smaller region, we can crop it. crop uses the extent of another object to achieve this.

# Chunk 18
chirps1_dist72 <- crop(x = chirpsz[[1]], y = districts %>% slice(72))

par(mar = c(0, 0, 0, 2))
chirps1_dist72 %>% plot(axes = FALSE, box = FALSE)
districts %>% st_geometry %>% plot(add = TRUE)
districts %>% st_centroid %>% st_coordinates %>% 
  text(x = ., labels = row.names(.))

The above uses the extent of district 72 (dist72) to crop the first layer of chirpsz. Note that in the plotting step we can pipe the cropped raster to plot, and also that we can label the district numbers on the plot by extracting their centroid coordinates and passing these into the “x” argument of text, and then using the row.names of the piped-in data.frame of centroid coordinates as the labels.

Cropping is important if we want to confine further analyses to a particular sub-region. However, if we just want to focus our plot to a particular region, then we can simply zoom the plot to that region (without cropping) using an extent object.

# Chunk 19
par(mar = c(0, 0, 0, 2))
plot(chirpsz[[1]], axes = FALSE, box = FALSE, ext = extent(districts[72, ]))
districts %>% st_geometry %>% plot(add = TRUE)
districts %>% st_centroid %>% st_coordinates %>% 
  text(x = ., labels = row.names(.))

# Chunk 20
plot_noaxes <- function(x, axes = FALSE, box = FALSE, mar = c(0, 0, 1, 4), 
                        ...) {
  if(!class(x) %in% c("RasterLayer", "RasterStack", "RasterBrick", "Extent")) {
    stop("This function is intended for rasters only", call. = FALSE)
  }
  par(mar = mar)
  plot(x, axes = axes, box = axes, ...)
}

# Chunk 21
plot_noaxes(chirpsz[[1]])
# chirpsz[[1]] %>% plot_noaxes  # also works in a pipeline

3.1.3 Aggregating/disaggregating

To change to resolution of a raster object, you can use aggregate to make a coarser resolution, or disaggregate to decrease the resolution. To make chirpsz match the 0.1 resolution of distsr (the rasterized districts), we do this:

# Chunk 21
chirpsz1agg <- aggregate(x = chirpsz[[1]], fact = 2, fun = mean)
chirpsz1agg
#> class      : RasterLayer 
#> dimensions : 99, 117, 11583  (nrow, ncol, ncell)
#> resolution : 0.1, 0.1  (x, y)
#> extent     : 21.95, 33.65, -18.1, -8.200001  (xmin, xmax, ymin, ymax)
#> crs        : +proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0 
#> source     : memory
#> names      : Y16299 
#> values     : 0, 12.18843  (min, max)

We aggregate the first layer of chirpsz by a factor of 2 (fact = 2), taking the average of the aggregated pixels (fun = mean). Since the starting resolution was 0.05, doubling the pixel size takes it to 0.1. We could have chosen to aggregate all layers, and we could have chosen a different aggregation function (e.g. sum, max).

To disaggregate, there are two options:

# Chunk 22
chirpsz1km <- disaggregate(x = chirpsz[[1]], fact = 5)
# chirpsz1km <- disaggregate(x = chirpsz[[1]], fact = 5, method = "bilinear") 
chirpsz1km
#> class      : RasterLayer 
#> dimensions : 985, 1170, 1152450  (nrow, ncol, ncell)
#> resolution : 0.01, 0.01  (x, y)
#> extent     : 21.95, 33.65, -18.05, -8.200001  (xmin, xmax, ymin, ymax)
#> crs        : +proj=longlat +datum=WGS84 +no_defs +ellps=WGS84 +towgs84=0,0,0 
#> source     : memory
#> names      : Y16299 
#> values     : 0, 18.00534  (min, max)

The first option is the default one, which just breaks apart each pixel into the number of smaller new pixels specified by the factor, assigning each new pixel the same value as its larger parent. Here we specified a factor of 5, leading to an output resolution of 0.01 (~1 km), and thus 25 times the number of pixels as in the original chirpsz[[1]] (run ncell(chirpsz1km) / ncell(chirpsz[[1]]) to see).

The second way (commented out), is to set method = bilinear, which interpolates during disaggregation. In this case, disaggregate does the job using the resample function, which we will see next.

3.1.4 Resampling

Resampling is done for many reasons, but one particularly common case is as a final step following aggregation or disaggregation, when it is needed to co-register the resulting grid to another grid.

# Chunk 23
chirps125 <- aggregate(x = chirpsz[[1]], fact = 5)  # no fun b/c default is mean
s <- stack(chirps125, farmersr)  # fails 

par(mar = c(1, 1, 1, 1))
plot(extent(chirps125), axes = FALSE, col = "blue")
plot(extent(farmersr), add = TRUE, col = "red")

After aggregating chirpsz layer 1, we try and fail to stack the result with farmersr, because (as the plot of extents show, and the warning tells) the two objects have different extents. So, another approach is needed:

# Chunk 24
farmersr_rs <- resample(x = farmersr, y = chirps125) 
s <- stack(chirps125, farmersr_rs)  
names(s) <- c("rain", "farmer_count")
plot_noaxes(s)

We resample farmersr to chirps125rs, since chirps125rs has the larger extent. However, there is one more thing we should do before using these data, and that is an adjustment to farmersr. Have a look at this:

plot_noaxes(s$farmer_count >= 0)
plot(st_geometry(st_union(districts)), add = TRUE)

This shows that there are no places where there are 0 farmers–because the original data contributing to farmersr (the second layer in s) was derived from point locations representing the approximate locations of where farmers were interviewed. The data thus have no points where there were 0 farmers interviewed (it would be silly to conduct an interview with no subject), thus everywhere outside of interview locations is assigned a no data value. These are not analyzed in raster operations. So we have to fix this if we want to have the full area of Zambia in the second layer of our stack.

s$farmer_count[is.na(s$farmer_count)] <- 0
s$farmer_count <- mask(s$farmer_count, s$rain)
plot_noaxes(s$farmer_count)
plot(st_geometry(st_union(districts)), add = TRUE)

Now all the areas in s$farmer_counts where no interviews were conducted area set to 0.

We can then stack and perform subsequent analyses that draw on both layers, e.g. finding areas where rainfall exceeded 1 mm and where there was more than 1 farmer:

# Chunk 25
plot_noaxes(s$farmer_count > 1 & s$rain > 1)
# (s$rain > 1 & s$farmer_count > 1) %>% plot_noaxes  # also works

3.2.1 Global statistics

The most basic analyses to perform on rasters is to calculate global summary statistics, i.e. statistics calculated across all cell values:

# Chunk 26
cellStats(x = chirpsz[[1]], stat = "mean")  # for a single date
cellStats(x = chirpsz[[c(5, 7, 14)]], stat = "mean")
summary(chirpsz[[1:3]])
#>              Y16299      Y16300       Y16301
#> Min.        0.00000     0.00000     0.000000
#> 1st Qu.     0.00000     0.00000     0.000000
#> Median      0.00000     0.00000     0.000000
#> 3rd Qu.     0.00000     0.00000     0.000000
#> Max.       18.00534    17.76521     8.853778
#> NA's    20995.00000 20995.00000 20995.000000

cellStats lets you calculate specific statistics from the cell values of a lone RasterLayer, or for a single, multiple, or all layers in a RasterStackBrick. summary (a generic) returns the quintile values and counts the number of NA or no data cells. Both functions by default remove NA values (which are in many if not most rasters), which is something that usually has to be specified when trying to apply these statistical functions to an ordinary vector, e.g. 

# Chunk 27
v <- values(chirpsz[[1]])
mean(v) 
#> [1] NA
mean(v, na.rm = TRUE)
#> [1] 0.6971701

v is a vector of all of the values from the first layer in the rainfall brick, including its NA values. mean returns an NA if you don’t tell the function to remove NA values first. This is important to remember, because both spatial and non-spatial data often have missing values, so you will have to deal with them explicitly in many cases.

Here’s a more programmatic way of using cellStats:

# Chunk 28
# #1
rain_stats <- lapply(list(mean, sum, sd, cv), function(x) {
  cellStats(x = chirpsz, stat = x)
})
names(rain_stats) <- c("mean", "sum", "sd", "cv")

# #2
rain_statsf <- do.call(cbind, rain_stats) %>% data.frame %>% 
  mutate(date = as.Date(gsub("Y", "", row.names(.)), "%y%j"))
# do.call(cbind, rain_stats) %>% data.frame
# do.call(cbind, rain_stats) %>% row.names %>% gsub("Y", "", .)
# do.call(cbind, rain_stats) %>% row.names %>% gsub("Y", "", .) %>%
#   as.Date(., "%y%j")

# #3
ps <- lapply(c("mean", "sum", "sd", "cv"), function(x) { # x <- "mean"
  ggplot(rain_statsf %>% dplyr::select(date, all_of(x))) + 
    geom_line(aes_string("date", x)) + xlab("")
})
cowplot::plot_grid(plotlist = ps)

In #1 we use lapply to calculate 4 different statistics over all dates in chirpsz, meaning that we get a time series for each statistic as calculated over all of Zambia.

In #2, we use a pipeline to bind the summary time series vectors into a data.frame (one statistic per column), and then do some gymnastics to convert the row names of the data.frame, which are constructed from the layer names of chirpsz (which are stored as “Y16XXX”, where XXX is the julian day) to a vector of dates. Work through the commented out code below this line, which breaks down the steps used to create the date variable. gsub first replaces the “Y” in each name, and then as.Date parses the remaining numbers into an actual date. The “%y%j” construction tells as.Date which parts of the character string relate to which part of a date: %y = two digit year; %j = julian day; placed next to one another %y%j means these two elements are immediately adjacent to one another in the string.

We use lapply to set up four ggplot objects in #3 (note the use of aes_string rather than aes, which allows the variable names to be passed as string, rather than unquoted), and then use cowplot::plot_grid to put those plots in a grid, using the “plotlist” argument to receive the input list of ggplots.

The results in the plot above are actually quite interesting. The top two panels show when the rainy season gets underway in earnest (just after Nov 8). The bottom two panels show two measures of variability, the standard deviation (SD) and coefficient of variation (CV, i.e. SD / mean). These two measures summarize the spatial variability of rainfall falling across Zambia on each day–SD increases as the amount of rain increases (which is expected–SD is usually positively correlated with the mean), whereas CV declines as rainfall increases, indicating that a progressively larger area of the country receives rainfall as the month progresses, so there is less spatial variability. There is a big spike in CV on November 8, which corresponds to a drop in mean and total rainfall. However, that drop masks the fact that there are a few small patches that received a decent amount of rainfall, thus leading to a high CV (see next plot below).

# Chunk 29
plot_noaxes(chirpsz[[15]], main = paste("CV =", round(rain_stats$cv[15])))

Another way to summarize raster data is visually, using a histogram (raster has a generic hist function)

# Chunk 30
par(mfrow = c(1, 3))
hist(chirpsz[[15:17]], col = "blue", xlab = "mm")

This variant plots a histogram per layer in the Raster* object (but we told it to plot 1 row, 3 columns, instead of the default (2 rows, 2 columns)).

freq is another way to summarize raster values that is similar to hist but without the automatic plot.

# Chunk 31
f <- freq(chirpsz[[1]]) %>% print()
#>       value count
#>  [1,]     0 21053
#>  [2,]     1   234
#>  [3,]     2   698
#>  [4,]     3   817
#>  [5,]     4   660
#>  [6,]     5   544
#>  [7,]     6   432
#>  [8,]     7   306
#>  [9,]     8   175
#> [10,]     9    59
#> [11,]    10    42
#> [12,]    11    41
#> [13,]    12    27
#> [14,]    13     7
#> [15,]    14     3
#> [16,]    15     2
#> [17,]    16     2
#> [18,]    18     1
#> [19,]    NA 20995

Here we apply freq to a dataset with continuous values, although this function is probably best reserved for categorical rasters. However, it produces reasonable results here.

3.2.2 Local statistics

The previous section showed us how to produce statistics calculated across the entire raster. Now we will learn to calculate local, or neighborhood, statistics.

# Chunk 32
# #1
# zonemu <- zonal(x = chirpsz, z = distsr, fun = "mean")  # fails b/c extent

# #2
distsr_rs <- resample(x = distsr, y = chirpsz, method = "ngb")  # match extent
zonemu <- zonal(x = chirpsz, z = distsr_rs, fun = "mean")
head(zonemu)[, 1:5]
#>      zone     Y16299    Y16300    Y16301    Y16302
#> [1,]    1 0.00000000 0.0000000 0.0000000 1.8976312
#> [2,]    2 0.01322501 0.0000000 0.0000000 0.0000000
#> [3,]    3 6.04584049 1.8021238 0.0000000 4.4494707
#> [4,]    4 0.00000000 0.3011147 0.0201552 0.0000000
#> [5,]    5 6.25742351 3.6532615 1.0868976 0.4739815
#> [6,]    6 0.00000000 0.0000000 0.0000000 0.0000000

# Chunk 33
distr_rfmu <- zonemu %>% data.frame %>% dplyr::select(1:2) %>% 
  subs(x = distsr_rs, y = ., by = "zone")
plot_noaxes(distr_rfmu)

# Chunk 34
# #1
wmat <- matrix(1 / 9, nrow = 3, ncol = 3) 
chirps1_focmu1 <- focal(x = chirpsz[[1]], w = wmat) 

# #2
wmat <- matrix(1, nrow = 3, ncol = 3) 
chirps1_focmu2 <- focal(x = chirpsz[[1]], w = wmat, fun = mean) 

# #3
wmat <- matrix(1, nrow = 5, ncol = 5) 
chirps1_focmu3 <- focal(x = chirpsz[[1]], w = wmat, fun = mean) 

# #4 
wmat <- matrix(1, nrow = 5, ncol = 5) 
chirps1_focmu4 <- focal(x = chirpsz[[1]], w = wmat, fun = mean, na.rm = TRUE) 

# #5
wmat <- matrix(1 / 9, nrow = 5, ncol = 5) 
chirps1_focmu5 <- focal(x = chirpsz[[1]], w = wmat, na.rm = TRUE) 

# plots
l <- list(chirps1_focmu1, chirps1_focmu3, chirps1_focmu4, chirps1_focmu5)
titles <- c("3X3 NAs not removed", "5X5 NAs not removed", 
            "5X5 NAs removed properly", "5X5 NAs removed improperly")
par(mfrow = c(2, 2))
for(i in 1:length(l)) {
  plot_noaxes(l[[i]], main = titles[i])
}

3.2.3 Analyzing the Z dimension

If we have a RasterStackBrick, we have three dimensions (x, y, z). Often we want to analyze the values in the Z dimension (which may represent time, spectral bands, or unrelated spatial predictors in a model) without altering the x and y dimensions.

The workhorse for doing this sort of analysis is calc, which allows you to apply pretty much any function to the Z-dimension of a RasterStackBrick.

# Chunk 35
# #1
rain_zmu <- calc(x = chirpsz, fun = mean)
rain_zsd <- calc(x = chirpsz, fun = sd)
rain_zrng <- calc(x = chirpsz, fun = range)

# #2
rain_zstack <- stack(rain_zmu, rain_zsd, rain_zrng)
names(rain_zstack) <- c("Mean", "StDev", "Min", "Max")

plot_noaxes(rain_zstack)

In #1 we pass mean, sd, and range to “fun” in calc. Note that range always returns two values, so calc conveniently returns a two-layer brick that contains the minimum in the first layer and the maximum in the second.

In #2 we then stack the three outputs, and rename the layers something meaningful so that plot_noaxes can plot them all at once.

You will see from the resulting plot that “Min” has only one value, 0, which makes sense for a rainfall time series (every pixel is likely to have at least one day of no rainfall over the course of a month).

3.3.1 Questions

1. How do cellStats, focal, and zonal differ from one another?

2. How do you disaggregate a raster with interpolation?

3. How do you run calc on images with different resolutions or extents?

3.3.2 Code

1. Run as.Date("10-11-2017", "%m-%d-%Y"), as.Date("10-11-17", "%m-%d-%y"), as.Date("101117", "%m%d%y"), and as.Date("10112017", "%m%d%Y") to get a better sense of date vectors work. Also try out lubridate::mdy("10-11-2017") and lubridate::as_date("20171011").

2. Convert farmers to a 0.1 degree raster (farmersr2) that contains the count of farmers per grid cell. Use distsr as the target raster so that the extents align.

3. Use zonal on farmersr2 to calculate the total number of farmers per district (use distsr to provide the zones), and then map them back onto the districts/zones using subs. Plot the result.

4. Use focal to calculate for chirpsz[[20]] the i) standard deviation within a 3X3 and 5X5 window, and ii) the maximum value in each 3X3 and 5X5 neighborhood. Do not remove NAs. Combine the results in a stack, as above, and then plot them using plot_noaxes.

5. Crop chirpsz[[1]] using the extent of districts[57, ], and disaggregate it to 0.01 resolution using both the default and bilinear methods. Plot the results side by side using plot_noaxes.

6. Use calc with chirpsz to calculate the total rainfall in the time series, the coefficient of variation, and the median. Stack the results and plot with meaningful titles using plot_noaxes (hint: name the layers of the stack), outputting plots on 1 row with 3 columns.